Finite Group Databasebeta

← #11860833

Subgroups — #11860833

Order 1152.

977 conjugacy classes of subgroups; only the 244 normal subgroups are shown.

normal subgroups only

This group has 977 conjugacy classes of subgroups — too many to draw. Only its 244 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594818C212yesmaximal
2C22×#3718C211yesmaximal, characteristic
3#10592821C211yesmaximal, characteristic
4C3×#5120C212yesmaximal
5#10591138C211yesmaximal, characteristic
6#10590791C214yesmaximal, complemented
7#10590790C214yesmaximal, complemented
8#78948—32nomaximal
9C22×C3×Dic6C2212yes—
10C2×C32×M16C2211yescharacteristic
11#64135C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C3×#926C2212yes—
14#63955—24no—
15#63843C2218yes—
16Dic3×Dic6—24no—
17C2×#3718C418yescomplemented
18C2×#3718C2212yes—
19C2×#3718C2212yes—
20#63642C2212yes—
21C8×C3⋊Dic3C2212yes—
22C3×#816C2218yes—
23#63576C2212yes—
24#63574C2212yes—
25#5812—32no—
26C22×#216—32no—
27#5516—32no—
28C3×#419—32no—
29#5122—32no—
30#5122—61no—
31#5120D312yes—
32#4998—32no—
33#4790—38no—
34#4789—38no—
35C22×C32×C4C2311yescharacteristic
36C22×C3×Dic3—22no—
37C2×C3×Dic6—22no—
38C2×C3×Dic6—24no—
39C2×C3×Dic6C2×C418yes—
40C2×C3×Dic6C2314yes—
41C32×M16—22no—
42C2×C32×C8C2312yes—
43#3757D412yes—
44C4⋊(C3⋊Dic3)D412yes—
45C4×C3⋊Dic3C2312yes—
46C2×C3⋊(C3⋊C8)C2×C414yes—
47C2×C3⋊(C3⋊C8)C2311yescharacteristic
48C2×C3⋊(C3⋊C8)C2311yescharacteristic
49C3×#217—22no—
50C3×C4⋊Dic3C2314yes—
51C3×C4×Dic3—22no—
52Dic3⋊Dic3—28no—
53Dic32—28no—
54#3718C2×C418yes—
55#3718C2×C418yes—
56#2950—91noSylow
57C22×C3×Q8—32no—
58C22×Dic6C2×D312yes—
59C2×C3×M16—21no—
60C2×C3×M16C2×D312yes—
61C3×#117—32no—
62Q8×Dic3—38no—
63Q8×Dic3—64no—
64C2×#216—316no—
65C2×#216—34no—
66C2×#216—34no—
67#926—32no—
68#926—61no—
69#926—64no—
70#926C2×D312yes—
71C22×C3⋊C8—32no—
72C22×C3⋊C8—61no—
73#887—38no—
74#877—64no—
75C4×Dic6—64no—
76C3×#103—38no—
77#816C2×D318yes—
78#815—34no—
79#815—62no—
80C8×Dic3—34no—
81C8×Dic3—62no—
82#808—34no—
83#807—34no—
84C23×C32C2×D411yescharacteristic
85C2×C32×C4C22×C412yes—
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4#4112yes—
88C2×C32×C4C2411yescharacteristic
89C2×C3⋊Dic3C2×D414yes—
90C2×C3×Dic3—28no—
91C2×C3×Dic3—24no—
92C2×C3×Dic3—24no—
93C3×Dic6—28no—
94C3×Dic6—24no—
95C3×Dic6C22×C418yes—
96C32×C8—22no—
97C3⋊(C3⋊C8)C22×C412yes—
98C3⋊(C3⋊C8)C22×C412yes—
99C22×Q16—91no—
100#519—92no—
101#441—94no—
102C4×Q16—94no—
103#427—91no—
104#419—32no—
105#405—91no—
106C2×C3×Q8—38no—
107C2×C3×Q8—34no—
108C2×C3×Q8—62no—
109C2×C3×Q8—64no—
110C22×C3×C4—21no—
111C22×C3×C4—62no—
112C22×C3×C4C22×D312yes—
113C22×Dic3—22no—
114C2×Dic6—22no—
115C2×Dic6—24no—
116C2×Dic6C4×D318yes—
117C2×Dic6C22×D314yes—
118C3×M16—24no—
119C3×M16—24no—
120C2×C3×C8—22no—
121C2×C3×C8C22×D314yes—
122C3×C4⋊C4—34no—
123C3×C22⋊C4—62no—
124C3×C42—62no—
125#217—22no—
126#217—34no—
127#217—62no—
128#216—316no—
129#216—316no—
130C4⋊Dic3—34no—
131C4⋊Dic3—62no—
132C4⋊Dic3—68no—
133C4⋊Dic3C22×D314yes—
134Dic3⋊C4—68no—
135C4×Dic3—22no—
136C4×Dic3—34no—
137C4×Dic3—62no—
138C4×Dic3—68no—
139C4×Dic3—68no—
140C2×C3⋊C8—38no—
141C2×C3⋊C8—32no—
142C2×C3⋊C8—32no—
143C2×C3⋊C8—61no—
144C2×C3⋊C8—61no—
145C2×C3⋊C8—64no—
146C22×C32—22no—
147C22×C32C4×D412yes—
148C22×C32C22×D411yescharacteristic
149C32×C4C4×D412yes—
150C32×C4C23×C411yescharacteristic
151C32×C4C2×#4111yescharacteristic
152C3⋊Dic3—24no—
153C3×Dic3—28no—
154C3×Dic3—44no—
155C22×Q8—32no—
156C2×Q16—98no—
157C2×Q16—92no—
158C2×Q16—92no—
159C2×M16D3211yescharacteristic
160C22×C8—91no—
161C4×Q8—98no—
162C4×Q8—184no—
163#117—32no—
164#117—91no—
165#117—184no—
166#107—92no—
167#106—92no—
168#103—38no—
169#97—92no—
170C4×C8—92no—
171C23×C3—21no—
172C23×C3D3×D412yes—
173C3×Q8—38no—
174C3×Q8—68no—
175C3×Q8—64no—
176C2×C3×C4—21no—
177C2×C3×C4—22no—
178C2×C3×C4—21no—
179C2×C3×C4—22no—
180C2×C3×C4—68no—
181C2×C3×C4—64no—
182C2×C3×C4—64no—
183C2×C3×C4C2×C4×D314yes—
184C2×C3×C4D3×D412yes—
185C2×C3×C4#23714yes—
186C2×C3×C4C23×D312yes—
187C2×Dic3—28no—
188C2×Dic3—24no—
189C2×Dic3—24no—
190C2×Dic3—38no—
191C2×Dic3—64no—
192Dic6—28no—
193Dic6—24no—
194Dic6C2×C4×D318yes—
195C3×C8—24no—
196C3×C8—24no—
197C3⋊C8—34no—
198C3⋊C8—34no—
199C3⋊C8—62no—
200C3⋊C8—62no—
201C2×C32—22no—
202C2×C32C2×C4×D411yescharacteristic
203C2×C32#57812yes—
204C2×Q8—34no—
205C2×Q8—38no—
206C2×Q8—62no—
207C2×Q8—64no—
208C22×C4—62no—
209C22×C4C2×D3211yescharacteristic
210Q16—98no—
211Q16—98no—
212M16—22no—
213C2×C8—91no—
214C2×C8—91no—
215C2×C8—94no—
216C2×C8C2×D3212yes—
217C4⋊C4—34no—
218C4⋊C4—92no—
219C4⋊C4—188no—
220C22⋊C4—62no—
221C22⋊C4—92no—
222C42—62no—
223C42—92no—
224C42—188no—
225C22×C3—24no—
226C22×C3—21no—
227C22×C3—22no—
228C22×C3—42no—
229C22×C3#67⋊C414yes—
230C22×C3C2×D3×D412yes—
231C3×C4—21no—
232C3×C4—21no—
233C3×C4—22no—
234C3×C4—68no—
235C3×C4—124no—
236C3×C4#67⋊C414yes—
237C3×C4C22×C4×D312yes—
238C3×C4C2×#23712yes—
239Dic3—28no—
240Dic3—44no—
241Dic3—68no—
242Dic3—124no—
243C32#295011yescharacteristic, complemented, Sylow
244C23#380211yescharacteristic
245Q8—38no—
246Q8—64no—
247Q8—68no—
248C2×C4—64no—
249C2×C4—68no—
250C2×C4—64no—
251C2×C4—94no—
252C2×C4C4×D3212yes—
253C2×C4#380211yescharacteristic
254C2×C4#380512yes—
255C2×C4C22×D3211yescharacteristic
256C8—22no—
257C8—92no—
258C8—92no—
259C2×C3—24no—
260C2×C3—22no—
261C2×C3—21no—
262C2×C3—42no—
263C2×C3C2×#67⋊C412yes—
264C2×C3#577914yes—
265C22—22no—
266C22#6390212yes—
267C22C2×#380211yescharacteristic
268C4—68no—
269C4—124no—
270C4—184no—
271C4#6390212yes—
272C4C2×C4×D3211yescharacteristic
273C4C2×#380511yescharacteristic
274C3—21no—
275C3#7894812yescomplemented
276C2—22no—
277C2#1059472312yes—
278C2C2×#6390211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutatorC32×C4C23×C4
FrattiniC2×C4C22×D32
FittingC2×C32×M16C22
socleC22×C32C22×D4
prime radicalC23×C32C2×D4
cosocleC2×C32×C4C24
hypercenterC2×M16D32
hypocenterC32#2950
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
6. #10590791C2semidirect
7. #10590790C2semidirect
17. C2×#3718C4semidirect
243. C32#2950semidirect
275. C3#78948semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#105948182
C22×#37182
#105928212
C3×#51202
#105911382
#105907912
#105907902
#789483